[Paper Review] Changes in the Distribution of Income Volatility

Shane T. Jensen, Stephen H. Shore|ArXiv.org|Aug 7, 2008

Financial Risk and Volatility Modeling21 references17 citations

TL;DR

This paper uses a Markovian hierarchical Dirichlet process to analyze time-varying income volatility in the U.S., revealing that the observed rise in average income volatility since the 1970s is driven almost entirely by a sharp increase in volatility among individuals already ex-ante identified as high-volatility types—primarily the self-employed and risk-tolerant individuals—while most others experience no significant change in volatility.

ABSTRACT

Recent research has documented a significant rise in the volatility (e.g., expected squared change) of individual incomes in the U.S. since the 1970s. Existing measures of this trend abstract from individual heterogeneity, effectively estimating an increase in average volatility. We decompose this increase in average volatility and find that it is far from representative of the experience of most people: there has been no systematic rise in volatility for the vast majority of individuals. The rise in average volatility has been driven almost entirely by a sharp rise in the income volatility of those expected to have the most volatile incomes, identified ex-ante by large income changes in the past. We document that the self-employed and those who self-identify as risk-tolerant are much more likely to have such volatile incomes; these groups have experienced much larger increases in income volatility than the population at large. These results color the policy implications one might draw from the rise in average volatility. While the basic results are apparent from PSID summary statistics, providing a complete characterization of the dynamics of the volatility distribution is a methodological challenge. We resolve these difficulties with a Markovian hierarchical Dirichlet process that builds on work from the non-parametric Bayesian statistics literature.

Motivation & Objective

• To investigate whether the observed rise in average income volatility since the 1970s reflects a uniform increase across individuals or is driven by a subset of the population.
• To address the methodological challenge of modeling time-varying, heterogeneous income volatility with grouped, longitudinal data.
• To examine whether individuals with high ex-ante volatility (based on past income changes) have experienced disproportionate increases in income volatility over time.
• To assess the role of self-employment and risk tolerance in shaping the distribution of income volatility trends.
• To evaluate the welfare implications of rising volatility by identifying which population segments are most affected.

Proposed method

• Employs a Markovian hierarchical Dirichlet process (MHDP) prior to model time-varying, heterogeneous income volatility parameters in a nonparametric Bayesian framework.
• Models income dynamics as a combination of permanent and transitory shocks, with variances (volatility) allowed to vary across individuals and over time.
• Uses a discrete, data-driven allocation of volatility parameters to L unique values, where L is inferred from the data, enabling nonparametric estimation of the volatility distribution.
• Incorporates time-dependency through a Markovian structure that models the probability of parameter changes from one year to the next within individuals.
• Applies a hierarchical prior to model group-level heterogeneity, accounting for individual-level clustering and time-series dependence in panel data.
• Estimates posterior distributions of volatility parameters using Bayesian inference, with results validated through weighted OLS regressions on posterior mean estimates.

Experimental results

Research questions

• RQ1 Is the rise in average income volatility since the 1970s representative of the entire population, or is it concentrated among a specific subgroup?
• RQ2 Do individuals who exhibited high income volatility in the past (ex-ante high-volatility types) show a disproportionate increase in volatility over time?
• RQ3 To what extent are the self-employed and risk-tolerant individuals responsible for the observed increase in income volatility?
• RQ4 How do trends in permanent versus transitory volatility differ across subgroups defined by income level, education, age, and risk tolerance?
• RQ5 What are the welfare implications of an increase in volatility that is concentrated among individuals most able to bear risk?

Key findings

• The increase in average income volatility is almost entirely driven by a sharp rise in volatility among individuals who were already ex-ante identified as high-volatility types based on past income changes.
• Self-employed individuals account for a substantial proportion of the overall increase in income volatility, with their volatility rising significantly more than that of other groups.
• Individuals who self-identify as risk-tolerant (with a coefficient of relative risk aversion less than 1/0.3) show a much larger increase in permanent income volatility compared to those who are not risk-tolerant.
• Transitory volatility shows no major differences in trend between risk-tolerant and non-risk-tolerant individuals, indicating the increase is primarily in permanent income risk.
• The increase in permanent volatility is greater for individuals with above-median income than for those with below-median income, though low-income individuals are over-represented among the most volatile.
• The increase in volatility at the right tail of the distribution is present across age groups and educational levels, indicating it is not confined to any single demographic subgroup.